Analysis of a Quadratic Finite Element Method for Second-Order Linear Elliptic PDE, With Low Regularity Data. (3rd April 2020) - Messaoudi, Rachid; Lidouh, Abdeluaab; Seddoug, Belkassem
Abstract: In the present work, we propose extend an approximation for the second order linear elliptic equation in divergence form with coefficients in L ∞ and L 1 -Data, based on the usual quadratic finite element techniques. We study the convergence with low-regularity solutions only belonging to W 0 1, q with q ∈ [ 1, d d − 1 [ and d ∈ { 2, 3 }, where the class of renormalized solution is considered as limit. Statements and proofs of linear finite elements approximation case in [1 ]; remain valid in our case, and when the Data is a bounded Radon measure, a weaker convergence is obtained. An error estimate in W 0 1, q is then deduced under suitable regularity assumptions on the solution, the coefficients and the L 1 -Data f .